{"total":137,"rows":[{"id":"2111.02801","title":"Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems","created":"2021-11-01","cited_by_count":222,"area":null},{"id":"2203.07404","title":"Respecting causality is all you need for training physics-informed neural networks","created":"2022-03-14","cited_by_count":156,"area":null},{"id":"2412.00568","title":"The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learning","created":"2024-11-30","cited_by_count":145,"area":null},{"id":"2308.08468","title":"An Expert's Guide to Training Physics-informed Neural Networks","created":"2023-08-16","cited_by_count":126,"area":null},{"id":"2410.13228","title":"From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning","created":"2024-10-17","cited_by_count":73,"area":null},{"id":"2307.00379","title":"Residual-based attention in physics-informed neural networks","created":"2023-07-01","cited_by_count":72,"area":null},{"id":"2501.16371","title":"Optimizing the Optimizer for Physics-Informed Neural Networks and Kolmogorov-Arnold Networks","created":"2025-01-22","cited_by_count":42,"area":null},{"id":"2104.10873","title":"Mosaic Flows: A Transferable Deep Learning Framework for Solving PDEs on Unseen Domains","created":"2021-04-22","cited_by_count":37,"area":null},{"id":"2205.01059","title":"Enhanced Physics-Informed Neural Networks with Augmented Lagrangian Relaxation Method (AL-PINNs)","created":"2022-04-29","cited_by_count":35,"area":null},{"id":"2405.04230","title":"Unveiling the optimization process of Physics Informed Neural Networks: How accurate and competitive can PINNs be?","created":"2024-05-07","cited_by_count":31,"area":null},{"id":"2209.03984","title":"$\\Delta$-PINNs: physics-informed neural networks on complex geometries","created":"2022-09-08","cited_by_count":28,"area":null},{"id":"2402.13412","title":"Scaling physics-informed hard constraints with mixture-of-experts","created":"2024-02-20","cited_by_count":24,"area":"moe"},{"id":"2306.17648","title":"Enhancing training of physics-informed neural networks using domain-decomposition based preconditioning strategies","created":"2023-06-30","cited_by_count":20,"area":null},{"id":"2204.05108","title":"Improved Training of Physics-Informed Neural Networks with Model Ensembles","created":"2022-04-11","cited_by_count":19,"area":null},{"id":"2310.04867","title":"Randomized Sparse Neural Galerkin Schemes for Solving Evolution Equations with Deep Networks","created":"2023-10-07","cited_by_count":18,"area":null},{"id":"2109.02035","title":"Variational Physics Informed Neural Networks: the role of quadratures and test functions","created":"2021-09-05","cited_by_count":17,"area":null},{"id":"2402.12475","title":"Diffeomorphism Neural Operator for various domains and parameters of partial differential equations","created":"2024-02-19","cited_by_count":15,"area":null},{"id":"2407.15727","title":"Inferring turbulent velocity and temperature fields and their statistics from Lagrangian velocity measurements using physics-informed Kolmogorov-Arnold Networks","created":"2024-07-22","cited_by_count":15,"area":null},{"id":"2207.14291","title":"Physics-Informed Neural Networks for Shell Structures","created":"2022-07-26","cited_by_count":13,"area":null},{"id":"2403.18494","title":"Learning in PINNs: Phase transition, diffusion equilibrium, and generalization","created":"2024-03-27","cited_by_count":13,"area":null},{"id":"2203.16577","title":"Calibrating constitutive models with full-field data via physics informed neural networks","created":"2022-03-30","cited_by_count":12,"area":null},{"id":"2410.01990","title":"Deep Learning Alternatives of the Kolmogorov Superposition Theorem","created":"2024-10-02","cited_by_count":12,"area":null},{"id":"2301.04480","title":"BINN: A deep learning approach for computational mechanics problems based on boundary integral equations","created":"2023-01-11","cited_by_count":11,"area":null},{"id":"2110.01359","title":"CENN: Conservative energy method based on neural networks with subdomains for solving variational problems involving heterogeneous and complex geometries","created":"2021-09-25","cited_by_count":10,"area":null},{"id":"2110.01601","title":"NeuFENet: Neural Finite Element Solutions with Theoretical Bounds for Parametric PDEs","created":"2021-10-04","cited_by_count":10,"area":null},{"id":"2107.11496","title":"Training multi-objective/multi-task collocation physics-informed neural network with student/teachers transfer learnings","created":"2021-07-24","cited_by_count":9,"area":null},{"id":"2311.00224","title":"Domain decomposition-based coupling of physics-informed neural networks via the Schwarz alternating method","created":"2023-11-01","cited_by_count":9,"area":null},{"id":"2403.03223","title":"Exact Enforcement of Temporal Continuity in Sequential Physics-Informed Neural Networks","created":"2024-02-15","cited_by_count":9,"area":null},{"id":"2301.11040","title":"Random Grid Neural Processes for Parametric Partial Differential Equations","created":"2023-01-26","cited_by_count":8,"area":null},{"id":"2404.17789","title":"BiLO: Bilevel Local Operator Learning for PDE Inverse Problems","created":"2024-04-27","cited_by_count":8,"area":null},{"id":"2506.04375","title":"Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient","created":"2025-06-04","cited_by_count":8,"area":null},{"id":"2304.04234","title":"Variational operator learning: A unified paradigm marrying training neural operators and solving partial differential equations","created":"2023-04-09","cited_by_count":7,"area":null},{"id":"2410.03496","title":"Fourier PINNs: From Strong Boundary Conditions to Adaptive Fourier Bases","created":"2024-10-04","cited_by_count":7,"area":null},{"id":"2211.03241","title":"Neural PDE Solvers for Irregular Domains","created":"2022-11-07","cited_by_count":6,"area":null},{"id":"2310.03861","title":"Variational Barycentric Coordinates","created":"2023-10-05","cited_by_count":6,"area":null},{"id":"2312.17329","title":"PINN surrogate of Li-ion battery models for parameter inference. Part I: Implementation and multi-fidelity hierarchies for the single-particle model","created":"2023-12-28","cited_by_count":6,"area":null},{"id":"2404.13646","title":"Physics-informed Discretization-independent Deep Compositional Operator Network","created":"2024-04-21","cited_by_count":6,"area":null},{"id":"2406.00238","title":"Robust Biharmonic Skinning Using Geometric Fields","created":"2024-06-01","cited_by_count":6,"area":null},{"id":"2504.01093","title":"Hard-constraining Neumann boundary conditions in physics-informed neural networks via Fourier feature embeddings","created":"2025-04-01","cited_by_count":6,"area":null},{"id":"2506.19805","title":"Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective","created":"2025-06-24","cited_by_count":6,"area":null},{"id":"2509.14198","title":"A Variational Framework for Residual-Based Adaptivity in Neural PDE Solvers and Operator Learning","created":"2025-09-17","cited_by_count":6,"area":null},{"id":"2302.01538","title":"DCEM: A deep complementary energy method for solid mechanics","created":"2023-02-03","cited_by_count":5,"area":null},{"id":"2310.10602","title":"Physics-informed neural wavefields with Gabor basis functions","created":"2023-10-16","cited_by_count":5,"area":null},{"id":"2401.17172","title":"Learning Domain-Independent Green's Function For Elliptic Partial Differential Equations","created":"2024-01-30","cited_by_count":5,"area":null},{"id":"2406.10997","title":"Two-level overlapping additive Schwarz preconditioner for training scientific machine learning applications","created":"2024-06-16","cited_by_count":5,"area":null},{"id":"2210.14402","title":"Adaptive deep density approximation for fractional Fokker-Planck equations","created":"2022-10-26","cited_by_count":4,"area":null},{"id":"2304.03552","title":"A physics-informed neural network framework for modeling obstacle-related equations","created":"2023-04-07","cited_by_count":4,"area":null},{"id":"2308.06709","title":"The Hard-Constraint PINNs for Interface Optimal Control Problems","created":"2023-08-13","cited_by_count":4,"area":null},{"id":"2411.03671","title":"Energy-based physics-informed neural network for frictionless contact problems under large deformation","created":"2024-11-06","cited_by_count":4,"area":null},{"id":"2510.08924","title":"AB-PINNs: Adaptive-Basis Physics-Informed Neural Networks for Residual-Driven Domain Decomposition","created":"2025-10-10","cited_by_count":4,"area":null},{"id":"2510.23810","title":"A Physics-informed Multi-resolution Neural Operator","created":"2025-10-27","cited_by_count":4,"area":null},{"id":"2205.03672","title":"Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions","created":"2022-05-07","cited_by_count":3,"area":null},{"id":"2210.13900","title":"Deep NURBS -- Admissible Physics-informed Neural Networks","created":"2022-10-25","cited_by_count":3,"area":null},{"id":"2311.15940","title":"Physics-informed neural networks for transformed geometries and manifolds","created":"2023-11-27","cited_by_count":3,"area":null},{"id":"2402.04390","title":"Densely Multiplied Physics Informed Neural Networks","created":"2024-02-06","cited_by_count":3,"area":null},{"id":"2403.13040","title":"Physics-Guided Neural Networks for Intraventricular Vector Flow Mapping","created":"2024-03-19","cited_by_count":3,"area":null},{"id":"2406.04170","title":"Element-wise Multiplication Based Deeper Physics-Informed Neural Networks","created":"2024-06-06","cited_by_count":3,"area":null},{"id":"2407.03647","title":"WANCO: Weak Adversarial Networks for Constrained Optimization problems","created":"2024-07-04","cited_by_count":3,"area":null},{"id":"2408.17298","title":"Accelerating the discovery of steady-states of planetary interior dynamics with machine learning","created":"2024-08-30","cited_by_count":3,"area":null},{"id":"2409.06560","title":"A Primer on Variational Inference for Physics-Informed Deep Generative Modelling","created":"2024-09-10","cited_by_count":3,"area":null},{"id":"2412.05719","title":"Finite Element Neural Network Interpolation. Part I: Interpretable and Adaptive Discretization for Solving PDEs","created":"2024-12-07","cited_by_count":3,"area":null},{"id":"2412.16644","title":"An explainable operator approximation framework under the guideline of Green's function","created":"2024-12-21","cited_by_count":3,"area":null},{"id":"2503.11196","title":"Physics-constrained DeepONet for Surrogate CFD models: a curved backward-facing step case","created":"2025-03-14","cited_by_count":3,"area":null},{"id":"2504.07976","title":"EquiNO: A Physics-Informed Neural Operator for Multiscale Simulations","created":"2025-03-27","cited_by_count":3,"area":null},{"id":"2505.07765","title":"Solving Nonlinear PDEs with Sparse Radial Basis Function Networks","created":"2025-05-12","cited_by_count":3,"area":null},{"id":"2210.14320","title":"FO-PINNs: A First-Order formulation for Physics Informed Neural Networks","created":"2022-10-25","cited_by_count":2,"area":null},{"id":"2310.02548","title":"Exact and soft boundary conditions in Physics-Informed Neural Networks for the Variable Coefficient Poisson equation","created":"2023-10-04","cited_by_count":2,"area":null},{"id":"2401.00033","title":"Hybrid Modeling Design Patterns","created":"2023-12-29","cited_by_count":2,"area":null},{"id":"2407.11183","title":"Differentiable Neural-Integrated Meshfree Method for Forward and Inverse Modeling of Finite Strain Hyperelasticity","created":"2024-07-15","cited_by_count":2,"area":null},{"id":"2411.16663","title":"Gaussian Process Priors for Boundary Value Problems of Linear Partial Differential Equations","created":"2024-11-25","cited_by_count":2,"area":null},{"id":"2412.01232","title":"Variational formulation based on duality to solve partial differential equations: Use of B-splines and machine learning approximants","created":"2024-12-02","cited_by_count":2,"area":null},{"id":"2505.03382","title":"Physics-informed neural network estimation of active material properties in time-dependent cardiac biomechanical models","created":"2025-05-06","cited_by_count":2,"area":null},{"id":"2505.20300","title":"FMEnets: Flow, Material, and Energy networks for non-ideal plug flow reactor design","created":"2025-05-10","cited_by_count":2,"area":null},{"id":"2507.17019","title":"Bayesian BiLO: Bilevel Local Operator Learning for Efficient Uncertainty Quantification of Bayesian PDE Inverse Problems with Low-Rank Adaptation","created":"2025-07-22","cited_by_count":2,"area":null},{"id":"2508.08309","title":"Variational volume reconstruction with the Deep Ritz Method","created":"2025-08-08","cited_by_count":2,"area":null},{"id":"2510.23501","title":"Training Deep Physics-Informed Kolmogorov-Arnold Networks","created":"2025-10-27","cited_by_count":2,"area":null},{"id":"2512.14941","title":"Boundary condition enforcement with PINNs: a comparative study and verification on 3D geometries","created":"2025-12-16","cited_by_count":2,"area":null},{"id":"2603.01762","title":"DGNet: Discrete Green Networks for Data-Efficient Learning of Spatiotemporal PDEs","created":"2026-03-02","cited_by_count":2,"area":null},{"id":"2211.15664","title":"Utilising physics-guided deep learning to overcome data scarcity","created":"2022-11-24","cited_by_count":1,"area":null},{"id":"2212.07462","title":"Harmonic (Quantum) Neural Networks","created":"2022-12-14","cited_by_count":1,"area":null},{"id":"2406.02645","title":"Astral: training physics-informed neural networks with error majorants","created":"2024-06-04","cited_by_count":1,"area":null},{"id":"2412.09453","title":"Finite-PINN: A Physics-Informed Neural Network with Finite Geometric Encoding for Solid Mechanics","created":"2024-12-12","cited_by_count":1,"area":null},{"id":"2501.18715","title":"chebgreen: Learning and Interpolating Continuous Empirical Green's Functions from Data","created":"2025-01-30","cited_by_count":1,"area":null},{"id":"2503.20222","title":"Solving 2-D Helmholtz equation in the rectangular, circular, and elliptical domains using neural networks","created":"2025-03-26","cited_by_count":1,"area":null},{"id":"2505.04875","title":"Physics-informed solution reconstruction in elasticity and heat transfer using the explicit constraint force method","created":"2025-05-08","cited_by_count":1,"area":null},{"id":"2508.02537","title":"Solved in Unit Domain: JacobiNet for Differentiable Coordinate-Transformed PINNs","created":"2025-08-04","cited_by_count":1,"area":null},{"id":"2510.03576","title":"BEKAN: Boundary condition-guaranteed evolutionary Kolmogorov-Arnold networks with radial basis functions for solving PDE problems","created":"2025-10-03","cited_by_count":1,"area":null},{"id":"2510.09670","title":"A physics-aware deep learning model for shear band formation around collapsing pores in shocked reactive materials","created":"2025-10-08","cited_by_count":1,"area":null},{"id":"2510.11987","title":"Nonlinear discretizations and Newton's method: characterizing stationary points of regression objectives","created":"2025-10-13","cited_by_count":1,"area":null},{"id":"2510.15177","title":"Finding geodesics with the Deep Ritz method","created":"2025-10-16","cited_by_count":1,"area":null},{"id":"2510.24557","title":"Enforcing boundary conditions for physics-informed neural operators","created":"2025-10-28","cited_by_count":1,"area":null},{"id":"2512.11184","title":"On the failure of ReLU activation for physics-informed machine learning","created":"2025-12-12","cited_by_count":1,"area":null},{"id":"2602.05849","title":"Visualizing the loss landscapes of physics-informed neural networks","created":"2026-02-05","cited_by_count":1,"area":null},{"id":"2602.13513","title":"Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization","created":"2026-02-13","cited_by_count":1,"area":null},{"id":"2603.02948","title":"Enhancing Physics-Informed Neural Networks with Domain-aware Fourier Features: Towards Improved Performance and Interpretable Results","created":"2026-03-03","cited_by_count":1,"area":null},{"id":"2605.04126","title":"Simultaneous CNN Approximation on Manifolds with Applications to Boundary Value Problems","created":"2026-05-05","cited_by_count":1,"area":null},{"id":"2605.10136","title":"Per-Loss Adapters for Gradient Conflict in Physics-Informed Neural Networks","created":"2026-05-11","cited_by_count":1,"area":null},{"id":"2605.10613","title":"Exact Fixed-Point Constraints in Neural-ODEs with Provable Universality","created":"2026-05-11","cited_by_count":1,"area":null},{"id":"2605.24278","title":"Fourier Feature Pyramids for Physics-Informed Neural Networks","created":"2026-05-22","cited_by_count":1,"area":null},{"id":"2207.00377","title":"Anisotropic, Sparse and Interpretable Physics-Informed Neural Networks for PDEs","created":"2022-07-01","cited_by_count":0,"area":null}],"next_cursor":"100"}